Existence of non-impulsive unique solution and stability for continuous-time linear rectangular descriptor Markov jump systems. (July 2020)

• Record Type: Journal Article
• Authors: Tian, Jiaming; Ma, Shuping
• Is Part Of: Automatica. Volume 117(2020)
• Publication Date: 2020-07
• Subjects: Stability analysis -- Impulse-free solution -- Rectangular descriptor systems -- Markov jump systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108953
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper investigates the existence of non-impulsive unique solution and stochastic stability problems for the continuous-time linear rectangular descriptor Markov jump systems (DMJSs) at two cases. For every case, the sufficient and necessary conditions, in terms of strict linear matrix inequalities (LMIs), are eventually proposed to guarantee that the continuous-time linear DMJSs are column (row) regular, column (row) impulse-free, stochastically stable and have a unique solution. In addition, with some assumptions satisfied, the conditions obtained in this paper can simultaneously ensure that there is no impulse in the solution at the instant when the Markov process jumps. Finally, two examples are provided to demonstrate the effectiveness of the results.